1. Field of the Invention
The present invention relates to a method for facilitating monitoring, in the of time, of the evolution of the physical states of an underground formation by and interpreting 4D seismic data.
2. Description of the Prior Art
Various aspects of the prior art are in the following publications:
Dumay, J., Foumier, F., 1988, xe2x80x9cMultivariate Statistical Analyses Applied to Seismic Facies Recognitionxe2x80x9d, Geophysics, 53, no9, pp. 1151-1159;
Sonneland, L. et al, 1997,  less than  less than  Seismic reservoir monitoring on Gullfalks greater than  greater than , The Leading Edge, 16, no9, pp. 1247-1252;
Ross C. et al  less than  less than  Inside the Crossequalization Blackbox greater than  greater than , The Leading Edge, 15 :11, 1996, pp. 1233-1240;
Kolmogorov A. N., 1950, Foundation of the Theory of Probability; Chelsea Publ. Co., New York;
Moore R. E., 1969, Interval Analysis: Prenctice-Hall, Englewood Cliffs;
Walley P., 1991, Statistical Reasoning with Imprecise Probabilities: Monographs on Statistics and Applied Probabilities n. 42, Chapman and Hall, London; as well as in patents French Patent 2,768,818 and U.S. patent application Ser. No. 09/949,930.
Seismic measurements are conventionally used to provide additional information, in relation to drilling data, on the variations of the subsoil formations: lithologic, petrophysical or fluid saturation variations. In particular, within the scope of hydrocarbon reservoir production, it has become quite frequent to record seismic measurements repeatedly and then to interpret the seismic measurement variations in connection with the saturation and pressure variations due to reservoir production phenomena. This interpretation is often carried out by means of statistical pattern recognition techniques allowing classification of the seismic events into various categories representing the different physical states of the reservoir. These approaches are for example described in the publication by Dumay, J., Fournier, F. (1988). Their application to the interpretation of repeated seismic surveys is for example described in the publication by Sonneland, L., et al. (1997).
One difficulty concerning interpretation of repeated (or 4D) seismic surveys is that the measurement is not perfectly repetitive. Thus, even in zones of the subsoil that are not affected by the production of the reservoir, and whose seismic response should remain unchanged in the course of time, seismic variations which only express the lack of reproducibility of the measurement are observed. Among the many causes, the variations of the seismic signal from one survey to the next, the variability of the acquisition noises between different surveys, the imprecise position of the pickups and of the seismic sources can be mentioned.
Despite extensive reprocessing efforts to homogenize the various measurement surveys before interpretation, by means of methods described in the aforementioned publication by Ross et al. (1996), a residual non-repeatability remains, which is not insignificant. Thus, at the level of the reservoir, part of the variation of the seismic response is due to this non-reproducibility of the measurement, the other part being of course related to the physical evolutions of the reservoir as a result of the production mechanisms.
It is therefore very important, in the interpretation of the 4D measurement, to take into account this uncertainty inherent in the measurement, and not related to the reservoir variations.
The method according to the invention facilitates identification of the changes, in the course of time, in the physical state of a first zone of an underground formation (a reservoir zone for example) from the changes detectable within a first time window on several seismic trace sets obtained respectively during successive seismic surveys, by taking account of the uncertainties on a certain number of descriptive seismic attributes, by reference to parts of the seismic traces of the various sets recorded in at least a second time window corresponding to at least a second zone of the underground formation (outside the reservoir) where the formation undergoes no significant physical state variation during the successive seismic surveys, wherein a discriminant analysis technique is used to classify seismic events located on the recorded traces into defined categories.
A fuzzy discriminant analysis technique, which is the object of the aforementioned patent U.S. patent application Ser. No. 09/949,930, is applied to the analysis of seismic events from the reservoir. The measurement uncertainties related to their imperfect reproducibility are first evaluated using jointly seismic observations of the various surveys, made outside the zone potentially affected by the production of hydrocarbons.
The method comprises:
forming a learning base comprising physical states that have already been recognized and classified into predetermined categories, each one being defined by attributes of known statistical characteristics,
constructing, by reference to the learning base, a classification function using a discriminant analysis technique, allowing distribution in the categories the various seismic events to be classified from available measurements on a certain number of attributes, this function being formed by determining the probabilities of belonging of the events to the various categories by taking account of uncertainties on the attributes in form of probability intervals of variable width, and assigning each seismic event to at least one of the predetermined categories according to the width of the probability intervals.
The uncertainties involved in the construction of the classification function are here uncertainties expressing the lack of reproducibility of the seismic attributes from one seismic survey to the next, which are obtained by statistical analysis of the attribute variations of the seismic events of the second time window.
According to an implementation mode, the learning base is formed from seismic events measured in the vicinity of wells drilled through the formation studied, by defining therefrom learning classes corresponding to different rock types or to different fluid contents, the various objects to be classified being associated with seismic attributes covering the formation, and for which the probability of belonging to each of the defined learning classes is evaluated in form of an interval whose boundaries depend on the seismic attributes and on the uncertainties on the attributes, these objects being assigned to at least one of the learning classes according to the relative width of the associated probability interval in relation to all of the probability intervals.
The learning base can be formed by selecting for example the seismic traces in the parts which are the most representative of the different supposed physical states of the first zone, and of their variations, obtained for example with a numerical flow and production simulation model.
The learning base can also be formed according to the modes of a multivariate probability density function calculated from all of the seismic events characterized by the selected attributes.
According to an implementation mode, the uncertainties on the seismic attributes of the first zone are estimated from the variations of the vertical mean of the attributes variations of the various seismic surveys in the second time window.
It is also possible to estimate the uncertainties on the seismic attributes in the first zone from three-dimensional stochastic simulations in order to reproduce, for the first zone, the spatial variability and statistical characteristics such as the mean and/or the variance, estimated by geostatistical analysis of the variations of the attributes in the various seismic surveys in the second time window.
According to an implementation mode, the evolution with time of the states of a system is monitored by remote sensing.
If necessary, the method can comprise preprocessing of the seismic traces so as to eliminate, on the trace parts of the successive trace sets included in the second time window, differences other than those related to the changes in the shape of the objects.
Taking account of the 4D uncertainties in the interpretation process leads to categories of the physical state of the reservoir that may be no longer recognized if the uncertainty on the measurements is too great, or to several possible categories, non-detectable as a result of the uncertainty level. The interpretation of the repeated seismic data which is thus made integrates then completely the non-reproducible aspect of this measurement type, and the random variations induced in the reservoir are no longer interpreted as physical variations of this reservoir.